Parental leave regulations and the persistence of the male breadwinner model: Using fuzzy-set ideal type analysis to assess gender equality in an enlarged Europe

his paper uses fuzzy-set ideal type analysis to assess the conformity of European leave regulations to four theoretical ideal typical divisions of labour: male breadwinner, caregiver parity, universal breadwinner and universal caregiver. In contrast to the majority of previous studies, the focus of this analysis is on the extent to which leave regulations promote gender equality in the family and the transformation of traditional gender roles. The results of this analysis demonstrate that European countries cluster into five models that only partly coincide with countries’ geographical proximity. Second, none of the countries considered constitutes a universal caregiver model, while the male breadwinner ideal continues to provide the normative reference point for parental leave regulations in a large number of European states. Finally, we witness a growing emphasis at the national and EU levels concerning the universal breadwinner ideal, which leaves gender inequality in unpaid work unproblematized.

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

After the Male Breadwinner Model? Childcare Services and the Division of Labor in European Countries

Fundamental reforms in childcare services appear to have eroded traditional
support to the male breadwinner model across European states. There has been a strong debate about the direction of these changes, and the ways in which childcare services can alter the division of labor and promote gender equality. This paper deals with these issues by using fuzzy set ideal-type analysis to assess the conformity of childcare service provisions in European economies to Fraser’s four ideal typical models: male breadwinner, caregiver parity, universal breadwinner, and universal caregiver. We find that there is resilience of traditional gender roles in the majority of European countries, while there are different variants of the universal breadwinner shaping different forms of childcare policies. The more equalitarian universal caregiver model maintains its utopian character.

A two-step approach for the analysis of hybrids in comparative social policy analysis: a nuanced typology of childcare policies

Typologies have represented an important tool for the development of comparative social policy research and continue to be widely used in spite of growing criticism of their ability to capture the complexity of welfare states and their internal heterogeneity. In particular, debates have focused on the presence of hybrid cases and the existence of distinct cross-national pattern of variation across areas of social policy. There is growing awareness around these issues, but empirical research often still relies on methodologies aimed at classifying countries in a limited number of unambiguous types. This article proposes a two-step approach based on fuzzy-set-ideal-type analysis for the systematic analysis of hybrids at the level of both policies (step 1) and policy configurations or combinations of policies (step 2). This approach is demonstrated by using the case of childcare policies in European economies. In the first step, parental leave policies are analysed using three methods – direct, indirect, and combinatory – to identify and describe specific hybrid forms at the level of policy analysis. In the second step, the analysis focus on the relationship between parental leave and childcare services in order to develop an overall typology of childcare policies, which clearly shows that many countries display characteristics normally associated with different types (hybrids and. Therefore, this two-step approach enhances our ability to account and make sense of hybrid welfare forms produced from tensions and contradictions within and between policies.

Towards Possibilistic Fuzzy Answer Set Programming

Fuzzy answer set programming (FASP) is a generalization of answer set programming to continuous domains. As it can not readily take uncertainty into account, however, FASP is not suitable as a basis for approximate reasoning and cannot easily be used to derive conclusions from imprecise information. To cope with this, we propose an extension of FASP based on possibility theory. The resulting framework allows us to reason about uncertain information in continuous domains, and thus also about information that is imprecise or vague. We propose a syntactic procedure, based on an immediate consequence operator, and provide a characterization in terms of minimal models, which allows us to straightforwardly implement our framework using existing FASP solvers.

Hidden Markov Models With Set-Valued Parameters

Hidden Markov models (HMMs) are widely used probabilistic models of sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, whose assessment can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we consider iHMMs under the strong independence interpretation, for which we develop efficient inference algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations, as well as performing filtering and predictive inference. Experiments with real data show that iHMMs produce more reliable inferences without compromising the computational efficiency.

Robust fuzzy Gustafson-Kessel clustering for nonlinear system identification

This paper deals with Takagi-Sugeno (TS) fuzzy model identification of nonlinear systems using fuzzy clustering. In particular, an extended fuzzy Gustafson-Kessel (EGK) clustering algorithm, using robust competitive agglomeration (RCA), is developed for automatically constructing a TS fuzzy model from system input-output data. The EGK algorithm can automatically determine the 'optimal' number of clusters from the training data set. It is shown that the EGK approach is relatively insensitive to initialization and is less susceptible to local minima, a benefit derived from its agglomerate property. This issue is often overlooked in the current literature on nonlinear identification using conventional fuzzy clustering. Furthermore, the robust statistical concepts underlying the EGK algorithm help to alleviate the difficulty of cluster identification in the construction of a TS fuzzy model from noisy training data. A new hybrid identification strategy is then formulated, which combines the EGK algorithm with a locally weighted, least-squares method for the estimation of local sub-model parameters. The efficacy of this new approach is demonstrated through function approximation examples and also by application to the identification of an automatic voltage regulation (AVR) loop for a simulated 3 kVA laboratory micro-machine system.

Risk assessment of E-Commerce projects using evidential reasoning

The purpose of this study is to develop a decision making system to evaluate the risks in E-Commerce (EC) projects. Competitive software businesses have the critical task of assessing the risk in the software system development life cycle. This can be conducted on the basis of conventional probabilities, but limited appropriate information is available and so a complete set of probabilities is not available. In such problems, where the analysis is highly subjective and related to vague, incomplete, uncertain or inexact information, the Dempster-Shafer (DS) theory of evidence offers a potential advantage. We use a direct way of reasoning in a single step (i.e., extended DS theory) to develop a decision making system to evaluate the risk in EC projects. This consists of five stages 1) establishing knowledge base and setting rule strengths, 2) collecting evidence and data, 3) determining evidence and rule strength to a mass distribution for each rule; i.e., the first half of a single step reasoning process, 4) combining prior mass and different rules; i.e., the second half of the single step reasoning process, 5) finally, evaluating the belief interval for the best support decision of EC project. We test the system by using potential risk factors associated with EC development and the results indicate that the system is promising way of assisting an EC project manager in identifying potential risk factors and the corresponding project risks.

Multiple Input Governor Control for a Diesel Generating Set

The paper presents a multiple input single output fuzzy logic governor algorithm that can be used to improve the transient response of a diesel generating set, when supplying an islanded load. The proposed governor uses the traditional speed input in addition to voltage and power factor to modify the fuelling requirements during various load disturbances. The use of fuzzy logic control allows the use of PID type structures that can provide variable gain strategies to account for non-linearities in the system. Fuzzy logic also provides a means of processing other input information by linguistic reasoning and a logical control output to aid the governor action during transient disturbance. The test results were obtained using a 50 kVA naturally aspirated diesel generator testing facility. Both real and reactive load tests were conducted. The complex load test results demonstrate that, by using additional inputs to the governor algorithm, enhanced generator transient speed recovery response can be obtained.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

Distinguished algebraic semantics for t-norm based fuzzy logics:Methods and algebraic equivalencies

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ?-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics-namely the class of algebras defined over the real unit interval, the rational unit interval, the hyperreals (all ultrapowers of the real unit interval), the strict hyperreals (only ultrapowers giving a proper extension of the real unit interval) and finite chains, respectively-and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and (strict) hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. © 2009 Elsevier B.V. All rights reserved.

The Inferential Complexity of Bayesian and Credal Networks

This paper presents new results on the complexity of graph-theoretical models that represent probabilities (Bayesian networks) and that represent interval and set valued probabilities (credal networks). We define a new class of networks with bounded width, and introduce a new decision problem for Bayesian networks, the maximin a posteriori. We present new links between the Bayesian and credal networks, and present new results both for Bayesian networks (most probable explanation with observations, maximin a posteriori) and for credal networks (bounds on probabilities a posteriori, most probable explanation with and without observations, maximum a posteriori).

An Efficient LS-SVM-Based Method for Fuzzy System Construction

This paper proposes an efficient learning mechanism to build fuzzy rule-based systems through the construction of sparse least-squares support vector machines (LS-SVMs). In addition to the significantly reduced computational complexity in model training, the resultant LS-SVM-based fuzzy system is sparser while offers satisfactory generalization capability over unseen data. It is well known that the LS-SVMs have their computational advantage over conventional SVMs in the model training process; however, the model sparseness is lost, which is the main drawback of LS-SVMs. This is an open problem for the LS-SVMs. To tackle the nonsparseness issue, a new regression alternative to the Lagrangian solution for the LS-SVM is first presented. A novel efficient learning mechanism is then proposed in this paper to extract a sparse set of support vectors for generating fuzzy IF-THEN rules. This novel mechanism works in a stepwise subset selection manner, including a forward expansion phase and a backward exclusion phase in each selection step. The implementation of the algorithm is computationally very efficient due to the introduction of a few key techniques to avoid the matrix inverse operations to accelerate the training process. The computational efficiency is also confirmed by detailed computational complexity analysis. As a result, the proposed approach is not only able to achieve the sparseness of the resultant LS-SVM-based fuzzy systems but significantly reduces the amount of computational effort in model training as well. Three experimental examples are presented to demonstrate the effectiveness and efficiency of the proposed learning mechanism and the sparseness of the obtained LS-SVM-based fuzzy systems, in comparison with other SVM-based learning techniques.